Answer
This polynomial is prime.
Work Step by Step
$x^2-8xy+64y^2$
This polynomial is prime because the perfect square trinomial formula says that
$(A\pm B)^{2}=A^{2}\pm 2AB+B^{2}$
In this example, $2AB=8xy\ne2\times x \times8y$.
If it were a perfect square trinomial, the middle term would be $16xy$.
